The Vatican named the two men as Francisco Jose Cox Huneeus and Marco Antonio Ordenes Fernandez, archbishop emeritus of the cities of La Serena and Iquique respectively.

A statement on Saturday explained that the decision was taken on Thursday and cannot be appealed. The notice also referred to a canonical measure relating to "manifest abuse of minors" as being the reason for dismissal.

Defrocking, officially called "reduced to the lay state", means they have been expelled from the priesthood.

It is the harshest punishment the Church can inflict on a member of the clergy and such action has rarely been taken against bishops.

In early October, the religious order to which Cox belongs, the Schoenstatt Fathers, said the Vatican was investigating an accusation against him relating to the sexual abuse of a minor in Germany in 2004.

Cox, who is believed to have returned to Germany after a period in Chile, could not be reached for comment.

According to Chilean media, Ordenes, who resigned as bishop of Iquique in 2012 while under Vatican investigation, was accused of molesting a 17-year-old altar boy.

He is believed to be living somewhere in Chile. It was not immediately possible to reach him for comment.

The announcement came shortly after Pope Francis met Chilean President Sebastian Pinera in Rome on Saturday.

Pinera said he had enjoyed a "very good, very intimate and very frank" discussion with the pontiff regarding the "difficult situation" Chile's Catholic Church was in.

"We share a hope that the church can undergo a true rebirth and regain the affection and closeness of its followers and can continue to play an important role in our country," he told reporters.

According to Pinera, Francis - who is from neighbouring Argentina - also touched on migration, the crises in Venezuela and Nicaragua and the environment during the conversation.

The defrockings come one day after the pope accepted the resignation of a US cardinal who was accused of covering up a sex abuse scandal in Pennsylvania.

A wide-ranging investigation

Allegations of abuse and cover-ups have dogged Chile's Catholic Church for years, but in recent months, an unprecedented investigation has ramped up efforts to identify victims and perpetrators.

More than 100 clergymen are under investigation in what is now the largest clerical sex abuse probe in Latin American history, spanning all of Chile's 15 mainland regions.

Prosecutors have raided church offices in five cities, uncovering evidence of abuses that were never reported to authorities.

The searches have so far identified 178 victims, 79 of which were minors at the time of the alleged abuse, and charged 167 members of the clergy with carrying out or covering up abuses.

Survivors and observers have expressed disbelief at the extent of the investigation, which has seen the highest-ranking member of Chile's Catholic Church - Cardinal Ricardo Ezzati - brought before the public prosecutor.

"I never thought they would touch the hierarchy of the church, much less bring a cardinal to testify," Issac Givovich, a 38-year-old victim, said.

"It's an achievement just to know that a prosecutor has dared touch him," he said.

Last month, Francis defrocked Father Fernando Karadima, the priest at the centre of the controversy over allegations he carried out decades of abuse against young boys.

Pope Francis and the Cardinals have offered to cooperate in the probe. However, the prosecutor leading the probe says any assistance has yet to materialise.

"There's been no cooperation, understood as voluntarily providing evidence or information, and we're still waiting for the Vatican to send information we requested," said Emiliano Arias.

"We haven't seen an attitude of active collaboration from the Vatican," he said.

Fernando Ramos, the secretary-general of Chile's Episcopal Conference - who also serves under Ezzati as auxiliary bishop of Santiago - said that, under Chilean law, the church is not obliged to inform secular authorities of knowledge of crimes.

However, according to Ramos, the church is working with the public prosecutor's office to reach an agreement on working together.

He said the church was seeking a balance between "responding to the necessity of state organisation to investigate these types of crimes and [the church's] internal rules".

"We are concerned with safeguarding the trust of those who came forward, who sometimes don't want their name or what happened to become public, so we need to protect that trust, which we have been shown," he said.

The ongoing scandal has damaged the reputation of both the Church and Pope Francis in Chile.

The pontiff drew sharp criticisim in the predominantly Catholic for controversially appointing Juan Barros, who is accused by Karadima's victims of witnessing and ignoring their abuse, as the bishop of Osorno.

A papal visit in January was marred by protests and calls for the pope to accept Barros' resignation, which had been offered several times.

In a shock move in May, all of Chile's 34 bishops resigned en mass over Francis' refusal to accept the resignation, following a crisis meeting.

So far, Francis has accepted seven resignations, not including the two bishops defrocked on Saturday.

In late September, the church was ridiculed for issuing a manual on clerical guidelines, which outlined "inappropriate" ways for clergy members to express affection, including kissing on the mouth, slapping individuals' backsides and touching their genitals.

The archdiocese later withdrew the manual from its website and apologised.

Ramos said the "unacceptable" abuse and alleged cover-ups, which have gradually come to light over the last decade, are "very deplorable".

"Evidently, this has really affected the reputation of the Catholic Church in Chile, as in other countries. It has helped us bring about a deep reflection on how we can adequately respond to these reports and also how we can prevent [abuse] continuing to happen," he said. "We weren't prepared to deal with it," he said.

"Firstly, we need to have clear and effective systems for coming forward [...] now effectively all dioceses have this system. The judicial systems that we have in the church also need to be reorganised so we are prepared to deal with these types of situations.

Thirdly, we need to support those who come forward and have a system of prevention where everyone in the church has responsibility for creating a safe and healthy environment," he said.

Chile's sex abuse scandal is part of a global crisis, which has cast a shadow over the moral authority of the Catholic Church.